ABSTRACT. We increase the complexity of visual tasks by considering vision through an ocean’s water surface. Seeing into water from above (e.g., space, aircraft) is important for remote sensing of coastal regions. Seeing into air from underwater is related to marine animal vision, and also can be used for a ‘virtual periscope’. We present models and methods for such tasks, accounting for reflection/refraction at the water surface, atmospheric effects, underwater scattering and random surface distortions. In particular, we explain how true object motion can be distinguished from the random dynamic motion of image projection caused by water waves, and how visual triangulation (by stereo or viewpoint motion) is possible in such rough conditions. Furthermore, we show how random light patterns on the sea floor, created by waves, lead to very accurate (and surprisingly simple) recovery of the underwater 3D structure.